Conformal Invariance in Physics |
In General > s.a. conformal structures [including
conformal Killing fields]; Scale Invariance.
* History: 1908, Bateman and
Cunningham discovered the form invariance of Maxwell's equations for electromagnetism
with respect to conformal spacetime transformations; The reasons for conformal
invariance were originally pointed out by H Weyl.
* Conformal invariance and Weyl invariance:
Conformal and Weyl invariance are sometimes taken to be synonymous, although it may be best
to distinguish conformal invariance of a theory in flat spacetime from the Weyl invariance
of a theory coupled to gravity, in curved spacetime.
* Conditions: In the absence of
dimensional parameters, conformal invariance requires the vanishing of
Taa.
* Special types: Restricted Weyl
invariance refers to transformations with conformal factor satisfying
∇2Ω = 0.
* And quantization: The conformal invariance
of a classical theory can be broken by quantization, as in the case of QCD with massless quarks.
@ General references: Flato et al AP(78) [covariance of field equations];
Boyanovsky & Naon RNC(90)
[in quantum field theory / statistical mechanics];
Zuber Rech(93)feb;
Nikolov & Todorov IJMPA(04) [and rationality of correlation functions];
Jackiw AIP(05)gq [examples in 3D];
Kastrup AdP(08)-a0808-in [historical developments];
Jackiw & Pi JPA(11) [in diverse dimensions];
Quirós et al GRG(13)-a1108 [formulation of principle of conformal equivalence, and applications];
László a1406-conf [without reference to a metric];
Mannheim a1506 [as an alternative to supersymmetry];
Todorov BJP-a1905 [hist].
@ Weyl vs conformal invariance:
Karananas & Monin PLB(16)-a1510;
Farnsworth et al JHEP(17)-a1702 [in quantum field theory];
Alvarez et al EPJC(19)-a1903 [spin-2].
@ Restricted Weyl invariance: Edery & Nakayama PRD(14)-a1406;
Edery & Nakayama MPLA(15)-a1502 [and Einstein gravity with cosmological constant and Higgs mass];
Oda a2005.
@ Spontaneous breaking: Smolin PLB(80) [and general relativity as low-energy limit];
Nieh PLA(82),
Venturi gq/06-MG11
[and generation of gravitational constant G];
Edery et al CQG(06)ht [Weyl theory + matter];
Kaplan et al PRD(09)-a0905 [as phase transition];
Schwimmer & Theisen NPB(11) [and trace anomaly];
't Hooft FP(11) [and elementary particle models without free parameters];
Hinterbichler & Khoury JCAP(12) [scale invariance, and cosmology];
Guendelman et al GRG(15)-a1408 [and cosmology];
't Hooft a1410-GRF [small-distance structure of gravity];
de Cesare et al EPJC(17)-a1612 [emergence of physical scales];
Ghilencea & Lee PRD(19)-a1809 [in model building beyond the Standard Model and inflation];
> s.a. conformal gravity; particle physics.
@ Generalizations: Pérez-Nadal EPJC(17)-a1609 [anisotropic conformal invariance];
> s.a. hořava gravity.
> Online resources:
see Wikipedia page.
Conformal Invariance in Gravity \ s.a. gravity
and gravitational theories [including scale invariant].
@ General references: Deser AP(70);
Bicknell JPA(76);
Suggett JPA(79),
JPA(79);
Dąbrowski et al AdP(09)-a0806 [rev];
't Hooft a0909-conf [conformal transformations in quantum gravity];
Moon et al MPLA(10)-a0912 [in Einstein-Cartan-Weyl space];
Nobili a1201,
a1201 [Conformal General Relativity];
Clark & Love MPLA(12)-a1205 [local Weyl scaling and dilatation invariance];
Quiros a1401 [physical consequences];
Rahmanpour & Shojaie GRG(16)-a1608 [metric measure spaces];
Nikolić a1702-conf
[conformal non-invariance of Einstein-Hilbert action];
Hobson & Lasenby a2008 [gauging].
@ And matter: del Campo et al JCAP(10)-a1006 [with dilaton, and spontaneous breaking of symmetry];
't Hooft a1011
[conformal constraint and the coupling to matter];
Padilla et al PRD(14) [scalar fields coupled to gravity];
Lucat & Prokopec CQG(16)-a1606 [and the standard model];
Shaposhnikov & Shkerin PLB(18)-a1803 [conformal symmetry breaking].
@ And cosmology: Kelleher CQG(04)gq/03,
CQG(04) [and the cosmological constant];
Cadoni PLB(06) [as broken by matter coupling, and the cosmological constant];
Mottola a1103-proc [and dark energy];
Nguyen a1111;
Bars et al PRD(14)-a1307
[lifting a non-scale-invariant theory to a Weyl-invariant one, and cosmology];
Barvinsky JCAP(14)-a1311 [ghost-free conformal extension of Einstein's theory, and dark metter];
Álvarez et al JCAP(15)-a1501;
Libanov et al JETPL(15)-a1508 [scalar perturbations];
Alexeyev & Krichevskiy PPNL-a2012 [inflationary solutions].
@ Related topics: Wei & Cai JCAP(07)ap/06 [and the Cheng-Weyl vector field];
Attard & Lazzarini NPB(16)-a1607 [and the Wess-Zumino functional].
> Various theories: see conformal gravity
[including spatial conformal invariance and quantum thory]; Shape Dynamics [evolving conformal
geometry]; teleparallel gravity; Weyl Invariance;
unified theories.
In Other Theories > s.a. Conformal Field Theory;
higher-spin theories; quintessence;
spin-2 fields; Stealth Fields.
@ Electromagnetism:
Rosen AJP(72)jul [conformal invariance of Maxwell's equations];
Wulfman a1003/JPA [consequences];
> s.a. electromagnetism in curved spacetime.
@ Standard model:
Meissner & Nicolai PLB(07);
Fabbri GRG(12)-a1107;
> s.a. electroweak theory.
@ Other theories:
Smirnov in(06)-a0708 [2D lattice models],
a0708 [Ising model];
Shaukat & Waldron NPB(10) [explicit coupling of theories to scale];
Andrzejewski & Gonera a1108 [mechanics];
Faci a1110 [constructing conformally invariant equations];
Hofman & Strominger PRL(11) [2D quantum field theory];
Casalbuoni & Gomis PRD(14)-a1404 [relativistic point particles];
Okazaki PRD(17)-a1704 [quantum mechanics];
Hammad et al a2012 [Klein-Gordon equation in curved spacetime].
> Related topics:
see anomalies; Biconformal Space;
mass [origin]; renormalization group.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 26 dec 2020